USB stick or portable hard drive?

swift1_2

You can setup your pc/laptop or have a NAS (network attached storage) i.e. a harddrive which is a direct connection to your router. You can set this up so that your family can access it directly over the internet and likewise they can setup something similar so that you can access files on their side. You can set it up so that they only have access to certain files and folders etc.

Some software you can use is xbmc - a free and easy to use media player, you can even use your android phone to use it as a remote control and view your content over the internet.

This way you can keep control of your content and not hand it over to these cloud companies.

The_Salad

I wouldn't post USB sticks or portable hard drives. Copy to a DVD and send that over. Much safer.

esuhl

As already mentioned, USB flash memory isn't considered a reliable archive medium, but the devices themselves aren't fragile, so are ideal for posting.

Mechanical hard drives are more reliable, but also more fragile, so posting them isn't ideal (but if it's cheap and you have backups, why not, I suppose).

You could use a file transfer service of some kind (e.g. Dropbox or 4shared), but it might be quicker to use FTP. You install an FTP server on your machine and share a folder, and your friends/family can run the FTP client and browse and download any files in that folder. It's a good way to transfer large files as you don't have to upload them to a third party before they can be downloaded by your family, although your PC would need to be on for them to be able to connect to you. FileZilla is a good free FTP client/server and has a pretty good setup guide.

Also, you can transfer files using remote access software like TeamViewer, which might be an option...